Question

In 1903, the winner of a competition was paid $50. In 2017, the winner's prize was $235,000. What will the winner's prize be in 2040 if the prize continues increasing at the same rate

Answer 1

Answer:

The prize in 2040 would be $1,293,986.

Step-by-step explanation:

We can calculate the annual increase rate as if it was a compound interest.

Then we have a period of 2017-1903=114 years, where the prize goes from $50 to $235,000.

We can then calculate this rate r as:

$FV=PV(1+r)^n\\\\\\r=\sqrt[n]{\dfrac{FV}{PV}} -1\\\\\\r=\sqrt[114]{\dfrac{235,000}{50}} -1\\\\\\r=\sqrt[114]{4700} -1\\\\\\r=1.077-1\\\\\\r=0.077$

We can calculate then the prize, increasing at the same rate, from 2017 to 2040.

The number of periods is n=2040-2017=23.

Then we have:

$FV=PV(1+r)^n\\\\FV=235,000(1.077)^{23}=235,000\cdot 5.5063=1,293,986$

The prize in 2040 would be $1,293,986.